Identifiability and Joint Recovery of a Structured Signal Ensemble From Sub-Nyquist Samples

Abstract

Efficient acquisition of correlated continuous-time signals is critical in applications such as distributed sensor networks and array processing. However, existing correlation models often fail to capture the shared structure of physical signals measured in close proximity. In this paper, we model each signal in an ensemble as the sum of a hidden common lowpass component and a signal-specific innovation highpass component with disjoint spectral supports, where the common bandwidth is unknown. We first derive theoretical identifiability conditions guaranteeing unique decomposition and reconstruction from subsampled observations. Further, we propose a practical recovery algorithm and a joint reconstruction framework that leverages parametric structured dictionaries parameterized by the unknown common bandwidth. Numerical experiments on an ensemble of four signals demonstrate exact reconstruction with a 25% aggregate sampling rate reduction under identifiability conditions, and robust recovery with up to a 74% rate reduction when all channels are sampled below the Nyquist rate, significantly reducing data acquisition and hardware overhead.